Motives of the Hitchin System

Explore advanced mathematical concepts in this Institute for Advanced Study lecture where Yale University's Junliang Shen delves into the topology of the Hitchin system and its connections to orbital integrals, non-abelian Hodge theory, and mirror symmetry. Learn how symmetries in these geometries are motivated by algebraic cycles, examining the proof of the motivic decomposition conjecture and the motivic "χ"-independence phenomenon for the Hitchin system. Discover the construction of algebraic cycles through the combination of Fourier-Mukai duality for the derived category of coherent sheaves and Springer theory, based on collaborative research with Davesh Maulik and Qizheng Yin.